Four-mirror systems with a very large aperture and a long focal length were investigated and designed. Their design idea is given. Through the derivation of primary aberration formula, the aberration properties were analyzed and discussed, and the method to determine its initial structure is reported. As examples, two four-mirror systems with spherical and parabolic primary mirror, 100m focal length, and 10m entrance pupil were optimally designed. Their imaging quality approaches diffraction limit within field of view of 0.4 and 0.5 degrees respectively.